"No, no," Gillibrand said with a broad smile. "I'm running for Senate as you know, Joy, and I do hope that New Yorkers will allow me to continue to serve."

"Oh, they will," Behar said. "I can see you in the White House."

Behar's remark was nothing new for Gillibrand, 51, a Democrat who succeeded Hillary Clinton as New York's junior senator in 2009 and is frequently and increasingly mentioned as a potential presidential candidate in 2020.

But if Gillibrand is to challenge President Donald Trump, first she has to win re-election this November. Republican challenger Chele Chiavacci Farley, 51, a veteran of the finance industry, stands in her way.

For her part, Gillibrand says she will serve a full Senate term if she's re-elected next month — which would keep her out of contention for 2020.

Running for a second full term

Gillibrand was elected twice to the U.S. House in the Albany area before rising to national prominence when she became then-Gov. David Paterson's surprise pick to replace Hillary Clinton in the Senate after Clinton was named secretary of state.

Since then, Gillibrand has easily won election twice: To fill out the remainder of Clinton's term in 2010 and to a full, six-year term in 2012.

In 2012, she took home 72 percent of the vote, besting Republican Wendy Long by more than 45 percentage points.

In an interview with the USA TODAY Network's Albany Bureau, Gillibrand ticked off a list of accomplishments during her Senate tenure.

Among them, she said she successfully pushed for benefits for 9/11 responders; banned insider trading by members of Congress; helped secure funding for job-training programs; led a push for the repeal of the military's "Don't Ask, Don't Tell" policy; and brought awareness to the issue of military sexual assault.

If elected to another term, Gillibrand said she would continue to push for a national paid-family-leave program and improved job-training programs, as well as advocate for the public funding of elections, a move she says would help get money out of politics.

“I think my agenda and what I’ve accomplished really goes to the heart and soul of what New Yorkers need and that’s why I’m going to keep fighting for those issues," Gillibrand said in an interview with the USA TODAY Network's Albany Bureau.

"That’s why I’m running for re-election.”

Progressive positions

Sen. Kirsten Gillibrand, D-N.Y., speaks during the New York State Senate debate hosted by WABC-TV, Thursday, Oct. 25, 2018 in New York. Gillibrand and Republican challenger Chele Farley have sparred in a televised debate over immigration, health care and whether the incumbent Democrat plans to run for her party's presidential nomination in two years. (AP Photo/Mary Altaffer, Pool)(Photo: Mary Altaffer, AP)

Gillibrand has taken a number of positions favored by the progressive wing of the Democratic Party, cosponsoring Sen. Bernie Sanders' "Medicare for All" bill and announcing in February she would no longer accept campaign contributions from corporate PACs.

She's also angered some within her party by saying President Bill Clinton should have resigned amid the Monica Lewinsky scandal and becoming the first Democratic senator to call for the resignation of Sen. Al Franken, which helped push Franken, a fellow Democrat, to quit following allegations he inappropriately touched women.

"I think that it’s important at this moment that we listen to women, hear their stories, give the opportunity for their allegations to be fully investigated, and believe women," Gillibrand told the Albany Bureau.

"With regards to Senator Franken, he was a friend and I was very disappointed but enough was enough."

Farley pushes back

Farley faces an uphill battle in New York, where Democrats outnumber Republicans by more than 2 to 1.

A partner at Mistral Capital International who previously worked for Goldman Sachs and UBS Capital, Farley has been a key fundraiser for the state Republican Party, becoming its finance chair last year.

Farley has sought to use Gillibrand's call to abolish the U.S. Immigration and Customs Enforcement agency against her, pointing to the rise of violent gang MS-13 on Long Island as reason to crack down on illegal immigration.

She's taken issue with a key provision of the Republican tax-reform plan — a $10,000 limit on deducting state and local taxes on federal returns — and faulted Gillibrand for not doing more to reach across the aisle and stop it.

She's called on Gillibrand to give back prior campaign contributions from corporations and Boies, Schiller & Flexner, a major law firm that once represented disgraced film mogul Harvey Weinstein.

And she's questioned whether Gillibrand is sincere about serving a full Senate term, accusing her of harboring national ambitions at the expense of her home state.

"She's moved so far to the left to try to appeal to these national liberal activists and coalitions," Farley said in an interview with the Albany Bureau.

She noted Gillibrand recently traveled to New Hampshire — a hotspot for presidential candidates — earlier this month to campaign for the Democratic candidate for governor.

"I've watched you and I know you're really working hard and, honestly, on the merits, you should win," Trump said.

Farley used her closing statement in the debate to call for term limits and again suggest Gillibrand has presidential ambitions.

Farley supports restricting senators to two, six-year terms.

"Senator Gillibrand has had her 12 years," Farley said. New York deserves a senator who is going to be focused on them, who is going to work hard for New York."

Gillibrand, meanwhile, has been reserved in her campaign spending, avoiding costly television advertisements in favor of social-media and other digital ads.

She spent about $11.8 million from 2013 through mid-October, according to Federal Election Commission data.

That's left her with about $10.6 million on hand — an amount that has further fueled speculation about 2020 and beyond.

Farley, by comparison, spent about $1.1 million and has about $195,000 on hand.

In her interview with the Albany Bureau, Gillibrand said she is entirely focused on New York, touting her travel around the state and the town halls she's held.

"I’ve visited 62 counties and done 16 town halls this summer and last summer so I can hear directly from constituents, and their stories are what informs my legislation, the things I fight for, the things I work on," she said.

"I think that’s what our democracy is supposed to be about.”

JCAMPBELL1@gannett.com

Jon Campbell is a correspondent for the USA TODAY Network's Albany Bureau.